Find the center angle of the AOB if it is 39 degrees greater than the inscribed angle ACB resting on the same arc.

The center angle is the angle whose vertex is located at the center of the circle.

An inscribed angle is an angle whose vertex lies on a circle and the sides intersect it.

Since the degree measure of the central angle ∠AOB is equal to the degree measure of the arc on which it rests, and the degree measure of the inscribed angle ∠ACB is equal to half of the corresponding arc, then:

∠АОВ = 2 ∠АСВ.

Thus, if:

∠АВВ = ∠АСВ + 39º, then:

∠АВ = 39º · 2 = 78º.

Answer: the degree measure of the central angle ∠АОВ is equal to 78º.